Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation
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PROGRAM PROG75
NUMBER OF STAGES AT LOW CONCENTRATIONS.
THIS PROGRAM CALCULATES THE NUMBER OF EQUILIBRIUM STAGES
USING THE SMOKER EQUATIONS.
IN THE LOW-CONCENTRATION REGION THE EQUILIBRIUM RELATION FOLLOWS
HENRY'S LAW AND Y=KX, AND THIS RELATIONSHIP IS USED TO PLOT THE
EQUILIBRIUM LINE IF DATA ARE NOT AVAILABLE. THE EQUATIONS
DEVELOPED BY SMOKER WILL HANDLE THESE OPERATIONS ANALYTICALLY.
******************************************************************
A1 = AVERAGE RELATIVE VOLATILITY OF THE RECTIFYING SECTION
A2 = AVERAGE RELATIVE VOLATILITY OF THE STRIPPING SECTION
R = REFLUX RATIO
XF = MOLE FRACTION OF THE FEED
XD = MOLE FRACTION OF THE TOP PRODUCT
XB = MOLE FRACTION OF THE BOTTOMS PRODUCT
N1 = NUMBER OF STAGES IN THE RECTIFYING SECTION
N2 = NUMBER OF STAGES IN THE STRIPPING SECTION
TOTAL = THE TOTAL NUMBER OF STAGES.
POST = THE OPTIMUM FEED STAGE LOCATION.
*******************************************************************
REAL K,KI,K2,NI,N2
COMMON/MASS/KI,K2
OPEN (UNIT=3, FILE='DATA75.DAT', STATUS='OLD', ERR=I8)
OPEN (UNIT=I, FILE='PRN')
READ THE RELATIVE VOLATILITIES OF THE TWO COMPONENTS AI, A2.
READ THE MOLE FRACTION OF THE FEED, XF.
READ THE MOLE FRACTION OF THE DISTILLATE, XD.
READ THE MOLE FRACTION OF THE BOTTOMS, XB.
READ THE REFLUX RATIO, R.
READ (3, *, ERR=I9) AI, A2
READ (3, *, ERR=I9) XF, XD, XB
READ (3, *, ERR=19) R
GO TO 5
WRITE (*, 23)
FORMAT (5X,'DATA FILE DOES NOT EXIST')
GO TO 999
WRITE (*, 29)
FORMAT (5X, 'ERROR MESSAGE IN THE DATA VALUE')
GO TO 999
WRITE (i, i00)
FORMAT (//, 15X , 49HEQUILIBRIUM NUMBER OF STAGES BY SMOKER' S EQUATION ,
* /IH ,TS(IIi*))
WRITE (I, ii0) AI, A2
FORMAT(5X,'THE RELATIVE VOLATILITY OF COMPONENT i.:', T60,
FI0.3,/,5X,'THE RELATIVE VOLATILITY OF COMPONENT 2.:'
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* T60,FI0.3)
WRITE (I, 120) XF, XD, XB, R
FORMAT(5X,'THE MOLE FRACTION OF THE FEED:', T60, FI0.4,/,
* 5X,'THE MOLE FRACTION OF THE DISTILLATE:', T60, FI0.4,/,
*
5X,'THE MOLE FRACTION OF THE BOTTOMS:', T60, FI0.4,/,
* 5X,'THE REFLUX RATIO:', T60, FI0.2)
GO TO i0
CALCULATE THE NUMBER OF STAGES IN THE RECTIFYING SECTION
s I=R/(
R+ 1.0 )
BI=XD/(R+I.0 )
CALCULATE K, THE VALUE OF THE X-ORDINATE AT THE POINT WHERE
THE EXTENDED OPERATING LINE INTERSECT THE VAPOUR-LIQUID
EQUILIBRIUM CURVE FROM THE QUADRATIC EQUATION AX^2+BX+C=0
CALCULATE THE CO-EFFICIENTS OF THE QUADRATIC EQUATION IN
THE RECTIFYING SECTION
A = S1"(A1-1.0)
B = SI+BI*(AI-I.0)-AI
C = B1
SOLVE THE QUADRATIC EQUATION
CALL PROGI (A, B, C, K)
CALCULATE THE NUMBER OF STAGES IN THE RECTIFYING SECTION, N1
C1 = 1.0+(AI-I.0)*K
X1 = XD-K
X2 = XF-K
BETA1 = (SI*CI*(AI-I.O))/(AI-(SI*(CI**2)))
VALI = (XI*(I.0-(BETAI*X2)))/(X2*(I.0-(BETAI*XI)))
VAL2 = AI/(SI*(CI**2))
CALCULATE THE NUMBER OF STAGES IN THE RECTIFYING SECTION.
NI=ALOG(VALI)/ALOG(VAL2)
WRITE (I, 130) N1
FORMAT(5X,'THE NUMBER OF STAGES IN THE RECTIFYING SECTION:'
T60, F8.2)
CALCULATE THE NUMBER OF STAGES IN THE STRIPPING SECTION, N2
$2 = ((R*XF)+XD-(R+I.0)*XB)/((R+I.0)*(XF-XB))
B2 = ((XF-XD)*XB)/((R+I.O)*(XF-XB))
CALCULATE THE CO-EFFICIENTS OF THE QUADRATIC EQUATION AX^2+BX+C=0
IN THE STRIPPING SECTION
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A = $2"(A2-I.0)
B = (S2+B2*(A2-1.0)-A2)
C = B2
CALCULATE THE NUMBER OF STAGES IN THE RECTIFYING SECTION.
CALL PROGI (A, B, C, K)
X3 = XF-K
X4 = XB-K
C2 = 1.0+(A2-1.0)*K
BETA2 = (S2*C2*(A2-1.0))/(A2-(S2*(C2**2)))
VAL3 = (X3*(I.0-(BETA2*X4)))/(X4*(I.O-(BETA2*X3)))
VAL4 = A2/($2"(C2"'2))
N2 = ALOG(VAL3)/ALOG(VAL4)
WRITE (i, 140) N2
FORMAT(5X,'THE NUMBER OF STAGES IN THE STRIPPING SECTION:',
T60, F8.2)
TOTAL = NI+N2
WRITE (I, 150) TOTAL
FORMAT(5X,'TOTAL NUMBER OF STAGES:', T60, F8.2)
THE FEED LOCATION IS THAT FROM THE STRIPPING SECTION TO
THE BOTTOM OF THE COLUMN.
POST = N2
WRITE (1, 160) POST
FORMAT (5X,'FEED STAGE LOCATION:', T60, F8.1)
WRITE (I, 170)
FORMAT (78(IH-))
FORM FEED THE PRINTING PAPER TO THE TOP OF THE NEXT PAGE.
WRITE (I, *) CHAR(12)
CLOSE (3,STATUS='KEEP')
CLOSE (i)
STOP
END
***************************************************************
THIS PROGRAM SOLVES THE QUADRATIC EQUATION AX^2+BX+C=0 IN THE
RECTIFYING AND STRIPPING SECTIONS
***************************************************************
SUBROUTINE PROG1 (A, B, C, K)
REAL K,K1,K2
COMMON/MASS/K1,K2
D = (B**2-4.0*A*C)
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IF
( D .LT.
0.0) THEN
GO TO i0
ELSE
El= (-B+SQRT(D))/(2.0*A)
K2= (-B-SQRT(D))/(2.0*A)
ENDIF
IF (KI .LT. 0.0 .OR. K1 .GT. 1.0) THEN
GO TO 20
ELSE
K = K1
GO TO 30
ENDIF
IF (K2 .LT. 0.0 .OR. K2 .GT. 1.0) THEN
GO TO 40
ELSE
K=K2
GO TO 30
ENDIF
WRITE (*, 190)
FORMAT(6X,'ROOTS ARE OUT OF LIMITS CHECK PROBLEM SPECIFICATION')
GO TO 3O
WRITE (*, 200)
FORMAT(6X,'IMAGINARY ROOTS, CHECK PROBLEM SPECIFICATION')
RETURN
END
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PROGRAM PROG76
RAPID ESTIMATES OF MULTICOMPONENT DISTILLATION AND
MINI~/M TRAYS IN DISTILLATION COLUMNS
THIS PROGRAM WILL CALCULATE THE FEED COMPONENT RECOVERY
IN BOTH THE COLUMN DISTILLATE AND BOTTOMS PRODUCTS AND
ESTIMATE THE MINIMUM NUMBER OF STAGES NEEDED TO PERFORM
THE GIVEN SEPARATION.
FEED STREAMS CONTAINING UP TO 12 COMPONENTS CAN BE HANDLED
BY THIS PROGRAM.
THE FOLLOWING ASSUMPTIONS FOR THIS PROGRAM ARE:
1. THERE IS ONLY ONE FEED STREAM WITH 12 OR FEWER COMPONENTS.
2. THERE IS ONLY ONE HEAVY KEY COMPONENT.
3. FEED COMPONENTS ARE ARRANGED IN ORDER OF DECREASING
RELATIVE VOLATILITY, WITH THE LIGHT KEY (LK) AND HEAVY KEY
(HK) COMPONENTS SHOWN ADJACENT TO EACH OTHER.
4. THE FEED ENTERS THE COLUMN AT THE OPTIMAL STAGE.
5. THE COLUMN PRODUCES TWO PRODUCTS (DISTILLATE AND BOTTOMS)
WITH OVERHEAD CONDENSER AND BOTTOM REBOILER.
********************************************************************
ALPHAi = RELATIVE VOLATILITY OF COMPONENT i
Ki = EQUILIBRIUM CONSTANT FOR COMPONENT i IN THE FEED STREAM
KHK = EQUILIBRIUM CONSTANT FOR HEAVY KEY COMPONENT
IN THE FEED STREAM
Di = COMPONENT i IN DISTILLATE, MOL
Bi = COMPONENT i IN BOTTOMS, MOL
BHK = HEAVY KEY COMPONENT IN BOTTOMS, MOL
FHK = HEAVY KEY COMPONENT IN THE FEED, MOL
DLK = LIGHT KEY COMPONENT IN DISTILLATE, MOL
FLK = LIGHT KEY COMPONENT IN THE FEED, MOL
ALPHA(LK)= RELATIVE VOLATILITY OF LIGHT KEY COMPONENT
Fi = COMPONENT i IN THE FEED
NUM1 = MINIMUM TRAYS AT TOTAL REFLUX
DHK = HEAVY KEY COMPONENT IN DISTILLATE, MOL
BLK = LIGHT KEY COMPONENT IN BOTTOMS, MOL
A,B = CORRELATION CONSTANTS
Q = FEED THERMAL CONDITION (RATIO OF LIQUID TO VAPOR
FOR THE FEED)
RECLK = THE PERCENTAGE RECOVERY OF THE LIGHT KEY COMPONENT
RECHK = THE PERCENTAGE RECOVERY OF THE HEAVY KEY COMPONENT
FACTOR = FACTOR FOR THE REFLUX RATIO (i.e. FACTOR*MREF)
FEED = THE POSITION OF THE FEED PLATE
CHOICE = DETERMINE WHETHER FEED IS EQUILIBRIUM CONSTANT OR
RELATIVE VOLATILITY.
***************************************************************
CHARACTER*5 CHOICE
DIMENSION ALPHA(20), B(20), D(20), F(20), PERD(20), PERB(20)
DIMENSION XF(20), XB(20), XD(20)
REAL K(20), MB(20), MD(20), NUMI, MREF
COMMON/DATAI/NI/M, F, K, RECLK, RECHK, KI, Q, FACTOR
COMMON/DATA2/THETA, FEED
OPEN (UNIT = 3, FILE='DATA76.DAT', STATUS='OLD', ERR=I8)
OPEN (UNIT =I, FILE='PRN')
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READ THE CHOICE OF PARAMETER e.g. RELATIVE VOLATILITY (REL) OR
EQUILIBRIUM CONSTANT (EQUIL).
READ THE TOTAL NUMBER OF COMPONENTS, NUM
READ THE FEED AND RELATIVE VOLATILITY OR EQUILIBRIUM CONSTANT, F,K
READ THE RECOVERIES OF LIGHT AND HEAVY KEYS, RECLK, RECHK.
READ THE POSITION OF THE HEAVY KEY COMPONENT, KI.
READ THE THERMAL FEED CONDITION, Q
READ THE FACTOR FOR THE REFLUX RATIO, FACTOR.
READ (3, 5, ERR=I9) CHOICE
FORMAT (A)
IF (CHOICE .EQ. 'REL' .OR. CHOICE .EQ. 'rel') THEN
READ THE TOTAL NUMBER OF COMPONENTS
READ (3, *, ERR=I9) NUM
READ THE FEED AND THE RELATIVE VOLATILITY OF EACH COMPONENT.
DO I = i, NUM
READ (3, *, ERR=I9) F(I), K(I)
END DO
ELSEIF (CHOICE .EQ. 'EQUIL' .OR. CHOICE .EQ. 'equil') THEN
READ THE TOTAL NUMBER OF COMPONENTS.
READ (3, *, ERR=Ig) NUM
READ THE FEED AND THE EQUILIBRIUM CONSTANT OF EACH COMPONENT.
DO I = i, NUM
READ (3, *, ERR=f9) F(I), K(I)
END DO
ENDIF
READ THE RECOVERIES OF THE LIGHT AND HEAVY COMPONENTS.
READ (3, *, ERR=I9) RECLK, RECHK
READ THE POSITION OF THE HEAVY KEY COMPONENT.
READ THE THERMAL CONDITION OF THE FEED.
READ THE FACTOR FOR THE REFLUX RATIO.
READ (3, *, ERR=I9) KI, Q, FACTOR
GO TO i0
WRITE (*, 22)
FORMAT (5X, 'DATA FILE DOES NOT EXIST')
GO TO 999
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WRITE (*, 23)
FORMAT (5X, 'ERROR MESSAGE IN THE DATA VALUE')
GO TO 999
ARRANGE THE FEEDS AND EQUILIBRIUM CONSTANT/RELATIVE
VOLATILITY IN THE ORDER OF DECREASING VALUE
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CALL SORT (K, F, NUM)
CHECK WHETHER EQUILIBRIUM CONSTANTS OR RELATIVE VOLATILITY
IS CHOSEN WITH THE FEED COMPONENTS
IF ( CHOICE .EQ. 'EQUIL' .OR. CHOICE .EQ. 'equil') THEN
GO TO 15
ELSEIF (CHOICE .EQ. "REL' .OR. CHOICE .EQ. 'rel') THEN
DO I = I, NUM
ALPHA(I)=K(I)
END DO
ENDIF
GO TO 25
CALCULATE THE RELATIVE VOLATILITIES OF THE COMPONENTS
EQUILIBRIUM VALUES OF THE LIGHT KEY AND HEAVY KEY COMPONENTS ARE:
DO I = i, NUM
ALPHA(I)=K(I)/K(KI)
END DO
CALCULATE THE CORRELATION CONSTANTS: AI,BI
AI=ALOGI0((I.0-RECHK)/RECHK)
VALI=(RECLK/(I.0-RECLK))*(RECHK/(I.0-RECHK))
BI=ALOGIO(VALI)/ALOGIO(ALPHA(KI-I))
CALCULATE THE COMPONENT MOLES IN THE DISTILLATE
DO I = I, NUM
D(I)=((10**AI)*(ALPHA(I)**BI))/(I.0+((10**AI)*(ALPHA(I)**BI)))
PERD(I)=D(I)*IO0.0
MD(I)=D(I)*F(I)
END DO
CALCULATE THE RECOVERY OF THE LIGHT KEY COMPONENT IN THE
DISTILLATE
K2=KI-I
D(K2)=F(K2)*RECLK
CALCULATE THE TOTAL MOLES IN THE DISTILLATE
SUMI=O. 0
DO I = 1, NUM
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SUMI=SUMI+MD(I)
END DO
CALCULATE THE PERCENTAGE RECOVERY IN THE BOTTOMS PRODUCT
DO I = I, NUM
B(I)=I.0/(I.0+((IO**AI)*(ALPHA(I)**BI)))
PERB(I)=B(I)*IO0.0
MB(I)=B(I)*F(I)
END DO
CALCULATE THE RECOVERY OF THE HEAVY KEY COMPONENT IN THE BOTTOMS
B(KI)=F(KI)*RECHK
CALCULATE THE TOTAL PRODUCT IN THE BOTTOMS
SUM2=0.0
DO I = i, NUM
SUM2=SUM2+MB(I)
END DO
CALCULATE THE MINIMUM NUMBER OF TRAYS IN THE COLUMN
VAL2=(MD(KI-I)/(MD(KI))*(MB(KI)/MB(KI-I)))
AMIN=ALOG(VAL2)/(ALOG(ALPHA(KI-I)))
RECLK=RECLK*I00.0
RECHK=RECHK*I00.0
CALCULATE THE MOLE FRACTIONS IN THE FEED,DISTILLATE AND BOTTOMS
SUMB=0.0
SUMD=0.0
SUMF=0.0
DO J = 1, NUM
SUMB=SUMB+MB ( J )
SUMD=SUMD+MD ( J )
SUMF=SUMF+F ( J )
END DO
DO I = I, NUM
XB ( I )=MB( I )/SUMB
XD ( I ) =MD ( I )/SUMD
XF ( I ) =F ( I )/SUMF
END DO
CALL UNDERW (NUM, Q, XF, XD, THETA, MREF, ALPHA, KI)
USE McCORMICK'S EQUATION TO DETERMINE GILLILAND'S GRAPHICAL
CORRELATION AND HENCE THE EQUILIBRIUM NUMBER OF STAGES.
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REF=FACTOR*MREF
X= ( REF-MREF ) / ( REF+I. 0 )
C=0.105*ALOGIO (X) +0.44
Y=I. 0- (X**C)
NUMI=(Y+AMIN)/( I. O-Y)
USE KIRKBRIDE'S EMPIRICAL EQUATION TO ESTIMATE THE POSITION
OF THE FEED PLATE.
ZI=(XF(KI)/XF(KI-I)*(SUM2/SUM1)*(XB(KI-I)/XD(KI))**2)
CI=0.206*ALOG10(ZI)
Z2=10"*CI
FEED=(Z2*NUM1)/(I.O+Z2)
CALL OUTPUT(NUM,F,ALPHA,PERD,MD,PERB,MB,KI,RECLK,RECHK,AMIN,
* SUM1,SUM2,MREF,REF,NUM1)
CLOSE (3, STATUS='KEEP')
CLOSE (i)
STOP
END
THIS PROGRAM CALCULATES THE FEED COMPONENTS IN ORDER
OF DECREASING RELATIVE VOLATILITY.
****************************************************************
SUBROUTINE SORT (X, Y, N)
DIMENSION X(20), Y(20)
NI=N-1
DO i0 I=I,NI
I1=I+1
DO 20 J=I1,N
IF(X(I) .GE. X(J)) THEN
GO TO 20
ELSE
HOLD=X(I)
X(I)=X(J)
X(J)=HOLD
HOLD=Y(I)
Y(I)=Y(J)
Y(J)=HOLD
ENDIF
CONTINUE
CONTINUE
RETURN
END
****************************************************************
THIS PROGRAM CALCULATES THE UNDERWOOD CONSTANT THETA, USING THE
BINARY SEARCH METHOD AND THE MINIMUM REFLUX RATIO
(i.e. AT AN INFINITE NUMBER OF PLATES)
****************************************************************
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SUBROUTINE UNDERW (N, Q, XF, XD, THETA, MREF, ALPHA, KI)
DIMENSION ALPHA(20), XF(20), XD(20)
REAL MREF,LHS
THETAI=ALPHA(KI)
THETA2=ALPHA(KI-I)
DO I0 I=i,20
THETA=0.5*(THETAI+THETA2)
LHS=Q-I.0
DO J = i, N
LHS=LHS+((ALPHA(J)*XF(J))/(ALPHA(J)-THETA))
END DO
IF (LHS .LT. 0.0) THEN
THETAI=THETA
GO TO i0
ELSEIF (LHS .GT. 0.0) THEN
THETA2=THETA
GO TO i0
ELSEIF (LHS .EQ. 0.0) THEN
GO TO 50
ENDIF
CONTINUE
MREF=- 1.0
DOK= i, N
MREF=MREF+ ( ( ALPHA ( K ) *XD ( K ) ) / ( ALPHA ( K ) -THETA ) )
END DO
RETURN
END
*****************************************************************
THIS PROGRAM OUTPUTS THE RESULTS ON THE SCREEN
*****************************************************************
SUBROUTINE OUTPUT(NUM,F,ALPHA,PERD,MD,PERB,MB,KI,RECLK,RECHK,AMIN,
*SUMI,SUM2,MREF,REF,NUMI)
DIMENSION F(20), ALPHA(20), PERD(20), PERB(20)
REAL MD(20), MB(20), NUMI, MREF
COMMON/DATK2/THETA, FEED
WRITE (*, i00)
FORMAT(25X,'MULTICOMPONENT SYSTEM FRACTIONATION')
WRITE (*, ii0)
FORMAT(80(IH*))
WRITE (*, 120)
FORMAT(/,IX,'COMPONENT',7X,'FEED',SX,'REL VOLATILITY',3X,
* 'DISTILATTE ',8X,'BOTTOMS ')
WRITE (*, 130)
FORMAT(IX,'NUMBER',9X,'MOLES',7X,'ALPHA',IOX,'%',SX,,MOLES,,8X,
*'%',6X,'MOLES')
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